Abstract
Two finite size Hubbard models in two dimensions are considered at half filling: a 2×2 square lattice and a 4×4 square lattice, both with periodic boundary conditions. In the elementary case of the 2×2 lattice it is shown that the eigenvalues of the Hamiltonian corresponding to a given simmetry can be found applying the variational approach directly to the one and two-body density matrices. In the case of a 4×4 lattice the allowed region of the relevant one-body and two-body density matrices is numerically determined and the ground state energy is computed for several values of the interaction.
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